As a TEM mode transmission line type resonator for a filter for high frequencies of VHF and SHF bands, a distributed constant half wave or quarter wave line has typically been used hitherto. A flat coaxial transmission line, a strip line or a microwave stripline is used as a transmission line, and the resonance frequency is determined only by the length of the line, while the resonance frequency is not related to the line impedance.
FIGS. 1A and 1B illustrate a top plan view and a cross-sectional view of a conventional half wave open-ended resonator used in a microwave integrated circuit. This resonator is manufactured by forming a ground-plane conductor 13 on one surface of a dielectric substrate 13 and a narrow conductor 11 on the other surface of the substrate 13. The impedance of the line is usually set to 50 ohms in order to readily provide impedance matching with respect to external circuits. The resonator of FIGS. 1A and 1B has a characteristic such that the width of the conductor or line 11 narrows as the dielectric constant of the substrate 12 increases if the thickness of the substrate 12 is kept constant. For instance, assuming that the substrate 12 thickness is 1.0 millimeter, the width expressed in terms of W equals 2.6 millimeters when the dielectric constant is 2.6, and W equals 1.0 millimeter when the dielectric constant is 9. Because the resistance per unit distance increases as the width W decreases, the Q of the resonator deteriorates due to the resistance loss.
Assuming the length of the double open-ended stripline of FIGS. 1A and 1B is expressed in terms of l, the resonance frequency f is given by: ##EQU1## wherein n is 1, 2, 3 . . . and
v.sub.g is the velocity of an electromagnetic wave which propagates along the transmission line.
The lowest resonance frequency is referred to as the fundamental resonance frequency and is expressed as f.sub.0. There exist innumerable resonance frequencies as indicated by the above formula, and the resonance frequencies other than the fundamental resonance frequency f.sub.0 are referred to as spurious resonance frequencies. The lowest spurious resonance frequency and the second lowest spurious resonance frequency are respectively expressed in terms of f.sub.s1 and f.sub.s2, and these f.sub.s1 and f.sub.s2 are given by: ##EQU2##
The above equations indicate that the spurious resonance frequencies equal the integral multiples of the fundamental resonance frequency f.sub.0. Therefore, if a resonator of this structure of FIGS. 1A and 1B is used in an output filter of an oscillator or the like, harmonics of the second, third and more orders can not be suppressed.
As an example of another conventional strip-line resonator, which has a harmonic-suppression characteristic, a resonator having a structure shown in FIG. 2 is known. This resonator has a structure such that the impedance at the center portion 52 of the half wave resonator is made higher, while the impedances at the both end portions 51 and 53 are made lower. Namely, the resonator has a structure such that the width W1 of the center portion 52 is made narrower than the width W2 of the tip portions 51 and 53. With this structure, it is possible to make the spurious resonance frequency equal a value which is over twice the fundamental frequency f.sub.0. However, since the width of the center portion of the line 11, at which the electric current is maximum, is narrow, the resonator of this structure has a drawback in that the loss therein is greater than that of a uniform-width resonator having a constant width throughout the entire line.
When the aforementioned conventional resonator of FIGS. 1A and 1B having a uniform-width line is used to construct a band pass filter, the filtering or attenuating characteristic of the band pass filter as shown in FIG. 3 will be shown by the graphical representation of FIG. 4. Namely, there are dips in the attenuation curve at the fundamental frequency, f.sub.0, twice the fundamental frequency 2f.sub.0, three times the fundamental frequency 3f.sub.0 and so on. Therefore, when such a conventional band pass filter constructed of a plurality of uniform-width lines is used in a device, such as a wide-band receiver, a spectrum analyser or the like, in which only a desired signal should be transmitted while suppressing or attenuating other signals to a sufficient level, extra filter(s) such as band stop filters for rejecting the frequency components of 2f.sub.0, 3f.sub.0 and so on, or a low pass filter for permitting the transmission of only the fundamental frequency component f.sub.0 is/are required.